Question

what is the length of the hypotenuse of a 30-60-90 triangle if the side opposite the 60-degree angle is $6\sqrt{3}$? (1 point) \bigcirc $2\sqrt{3}$ \bigcirc $12\sqrt{3}$ \bigcirc 12 \bigcirc 6

Explanation:

Step1: Recall 30-60-90 triangle ratios

In a 30-60-90 triangle, the sides are in the ratio \(1 : \sqrt{3} : 2\), where the side opposite 30° is \(x\), opposite 60° is \(x\sqrt{3}\), and hypotenuse is \(2x\).

Step2: Set up equation for side opposite 60°

Given the side opposite 60° is \(6\sqrt{3}\), so \(x\sqrt{3}=6\sqrt{3}\).

Step3: Solve for \(x\)

Divide both sides by \(\sqrt{3}\): \(x = \frac{6\sqrt{3}}{\sqrt{3}} = 6\).

Step4: Find hypotenuse

Hypotenuse is \(2x\), so \(2\times6 = 12\).

Answer:

12 (corresponding to the option "12")